Some cheeses get crumbly when thawed back out. Shredded cheese seems to freeze just fine. Guess it depends more on what you intend to use it for after thawing. Never had a problem freezing hard cheese like Asiago or Parmesian. Feta gets crumbly, not much different than the way we use it. Some of the softer cheeses seem to change texture. Mozzarella, Colby, Muenster, etc.
Texture can change when freezing, I assume due to moisture changing when frozen.
We buy blocks of mozzarella and cut them into chunks and freeze them. Once they defrost we shred them so it doesnt really matter much. But if i were to cut it up for say pasta salad or a cheese platter thats a different story.
How are you planning to use the cheese once you defrost it?
I have also purchased an entire wheel of sharp. I never froze, though I did vacuum pack several chunks and stored in fridge and also a piece in my basement. I figured I would age it even more... it aged alright. A year later one pack almost popped from gasses building in it. One the oil separated from cheese. The one in the basement was inedible... I now take a half wheel and try to use up in 6 months. Wrapped in wax paper in zip-lock bag seems to store it fine in refrigerator.